Question

If $x+\sqrt{5}=4+\sqrt{y}$ , then $x+y=$ ______. (where $x$ and $y$ are rational)

• A. 9
• B. 10
• C. 11
• D. 12

Answer 1

The correct option is A

9

Finding the value of $x+y:$

We have:

$x+\sqrt{5}=4+\sqrt{y}$

Now comparing the rational and irrational parts of the LHS to RHS, we get,

$x=4\mathrm{and}y=5$

Therefore,

$$\begin{gathered} x+y=4+5 \\ \Rightarrow x+y=9 \end{gathered}$$

Hence, option A is correct.